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Abstract

In this study, transparent conducting nanocrystalline ZnO:Ga (GZO) films were deposited
by dc magnetron sputtering at room temperature on polymers (and glass for comparison).
Electrical resistivities of 8.8 × 10-4 and 2.2 × 10-3 Ω cm were obtained for films deposited on glass and polymers, respectively. The crack
onset strain (COS) and the cohesive strength of the coatings were investigated by
means of tensile testing. The COS is similar for different GZO coatings and occurs
for nominal strains approx. 1%. The cohesive strength of coatings, which was evaluated
from the initial part of the crack density evolution, was found to be between 1.3
and 1.4 GPa. For these calculations, a Young's modulus of 112 GPa was used, evaluated
by nanoindentation.

Introduction

Doped ZnO thin films are widely used as transparent electrodes in optoelectronic and
electro-optic devices such as solar cells and flat panel displays [1-3], because of their unique properties, specifically low electrical resistivity and
high transmittance in the visible spectral region [4]. These properties are obtained using substrate temperatures higher than 200°C, but
growing interest in flexible substrates has led to the use of polymeric alternatives,
which require the deposition of films at low temperature [5]. Furthermore, the deposition on polymeric substrates decreases the quality of the
film properties [6]; therefore, the pursuit toward an understanding of the structural, electromechanical
and electro-optical properties of nanocrystalline (nc) thin films is crucial for device
applications.

Experimental details

ZnO:Ga (GZO) thin films were deposited by dc-magnetron sputtering on glass and polyethylene
naphthalate (PEN) substrates, under an Ar atmosphere with a base pressure of 2 × 10-4 Pa, from a GZO target (zinc oxide/gallium oxide, 95.5/4.5 wt.%) of 2" diameter. A
target current density of 0.6 mA/cm2 was applied, and a deposition rate of 21 nm/min was obtained. No bias was applied
to the substrate holder during the depositions, which took place at room temperature.
The working pressure (Pw) was varied from 0.41 to 0.86 Pa, with the target-to-substrate distance kept at a
constant 8 cm. The crystallinity and crystal orientation was studied using a Bruker
AXS Discover D8 (Madison, USA) for X-ray diffraction (XRD). Glass substrates were
used to avoid the presence of polymer substrate peaks. The electrical resistivity,
carrier concentration and Hall mobility of the coatings on glass substrates were all
measured using Van der Pauw geometry under a magnetic field of 1 Tesla. The electromechanical
tests were carried out on 10 × 40 mm2 samples using a computer-controlled tensile testing machine (Minimat, Polymer Labs,
Loughborough, UK), which was mounted on an optical microscope stage (Nikon Optiphot-100,
Tokyo, Japan). One of the grips of the instrument was displaced at a constant speed
of 0.2 mm/min. The applied load and stage displacement values were recorded at 1-s
intervals. Crack development was recorded through a CCD camera connected to the microscope,
with the evolution of the crack density obtained by the subsequent video analysis.
The thickness of the polymer substrates was measured using a Fischer Dualscope MP0R
instrument (Sindelfingen, Germany).

Results and discussion

Structural characterization

Figure 1a shows the XRD spectra obtained for nc GZO thin films (approx. 100-nm thick) as a
function of the Pw, where only the ZnO (002) peak, at approx. 34°, is observed. The spectra reveal a
highly textured hexagonal phase with a wurtzite structure. A lower Pw resulted in samples with a higher c-lattice parameter. In the thin films prepared
with a Pw, between 0.41 and 0.86 Pa, the (002) peak position shifted from 2θ = 33.93° (c = 0.528 nm) to 2θ = 34.06° (c = 0.525 nm). The full-width at half-maximum (FWHM) can be expressed as a linear combination
of the lattice strain and crystalline size. The effects of strain and particle size
on the FWHM can be expressed as [7]

where β is the measured FWHM, θ is the Bragg angle of the peak, λ is the X-ray wavelength
(1.5418 Å), ε is the effective particle size and τ is the effective strain. The average
particle size, calculated from the plot cos θ versus sin θ shown in Figure 1b, was 8.7 nm. The particle size (Dv) calculated from Scherrer's formula (Dv = 0.94λ/(β cos θ)), was 8.9 nm, which is very close to that calculated from Equation
1 [8]). The presence of strain in the ZnO crystal lattice, caused indirectly by Pw, can be expected to exert significant influence on the mechanical properties of the
nc-GZO thin film.

Optical properties

The nc nature of the thin films influences both optical and electrical performance.
Figure 2 shows optical transmittance as a function of wavelength for thick GZO films (approx.
700 nm) prepared on glass at various Pw, using air as a reference. The near infra-red transmittance is lower for Pw values of 0.41 and 0.53 Pa and increases with higher Pw, which is consistent with the changes observed in the electrical resistivity (discussed
in the next section). The optical band gap for GZO films was calculated by plotting
(αhν)2 as a function of photon energy (hν) and extrapolating the linear region of (αhν)2 to energy axis where (αhν)2 corresponds to zero. Figure 2b shows the plot of (αhν)2 as a function of photon energy (hν) for GZO films. From these plots, it can be seen that the value of the bandgap of
GZO decreased from 3.73 eV (0.41 Pa) to 3.48 eV (0.86 Pa), which can be understood
in the context of the Burstein Moss shift [9].

Electrical properties

The electrical resistivity, charge carrier concentration and Hall mobility as a function
of the Pw, for GZO films deposited on glass, are shown in Figure 3. The resistivity of GZO samples decreased initially, and then increased with the
Pw. In general, the average resistivity was low (approx. 10-4 Ω cm), which can be attributed to high carrier concentration. Considering the similarity
in the conduction mechanism of electrons in GZO and ITO, the grain boundary (GB) and
ionized impurity scattering processes can be considered the two dominant mechanisms,
limiting electron transport in nc-GZO films, as in the case of ITO, where other scattering
mechanisms such as lattice vibrations and neutral impurity scattering may typically
be neglected [10]. The relative importance of the scattering mechanism is dependent on film quality
and carrier concentration. Unlike intrinsic ZnO, where the conduction is generally
controlled by GB-scattering, in doped ZnO at high electron density (>1020 cm-3), the ionized impurity scattering can be expected to dominate, which explains the
low values of electron mobility (<10 cm2V/s) [11].

Figure 3.The electrical resistivity, carrier concentration and Hall mobility for GZO/glass
as a function of the Pw.

Tensile tests

Tensile tests were performed at a constant strain rate on PEN substrates (82 μm) coated
with GZO films (approx. 100 nm) prepared under two different Pws to increase nominal strains. The PEN substrate is isotropic, and the elastic modulus
was 4.23 GPa, as measured through the tensile test on uncoated substrate. The cracking
densities as a function of the substrate nominal strain for two different GZO coatings
(0.53 and 0.86 Pa) are shown in Figure 4a. The crack densities at saturation of these two PEN/GZO films were 0.316 and 0.515
μm-1, respectively. The coatings have similar properties and thicknesses, with small differences
causing variations wholly within acceptable margins of error. Using the weakest link
model, the coating's cohesive strength was evaluated from the early stages of the
fragmentation process, assuming a Weibull-type, size-dependent probability of failure
for the coating fragments of length ℓ under a stress σ [12,13]:

Figure 4.Cracking density as a function of the substrate nominal strain for different GZO coatings
deposited on PEN (82 μm) and the crack density evolution of the PEN/GZO coatings.

(2)

Assuming that the residual stresses were negligible, in the initial stage of fragmentation,
the average fragment length was related to the stress acting in the coating. The average
fragment length (ℓ) is ℓ0(σ/β)-α, where a normalizing factor (ℓ0) of 1 μm was chosen. In addition, σ is the axial stress acting in the coating, and
α and β are the Weibull shape and scale parameters, respectively. These parameters
were derived from a plot of ln(ℓ) versus ln(σ), shown in Figure 4b, using the initial part of the crack density evolution of the PEN/GZO coatings, displayed
in Figure 4a.

The cohesive strength of the coating at critical length (ℓc) can be expressed as

(3)

where Γ is the gamma function, ℓc = (3/2)ℓsat is the critical length and ℓsat is the experimental mean fragment length at saturation, which is also the inverse
of the crack density at saturation [14]. As shown in Figure 4a, the GZO coatings prepared at Pw of 0.53 and 0.86 Pa revealed mean fragment lengths at saturation of 3.11 and 1.94
μm, respectively.

In order to take into account its influence, the internal stress was evaluated, and
the COS and the coating strength obtained with this method were corrected.

(4)

where σi is the internal stress and εi= σi(1 - νc)/Ec, the internal strain, with Ec and νc being the Young's modulus and Poisson ratio, respectively, of the coating. Young's
modulus of GZO was measured by nanoindentation at 113 and 112 GPa from samples prepared
at 0.60 and 0.86 Pa, respectively. Young's modulus of the PEN substrate was determined
from tensile testing (4.23 GPa). The cohesive strength of the coatings, which was
evaluated from the initial part of the crack density evolution, was found to be between
1.3 and 1.4 GPa. The crack onset strains (COScor) occurs for nominal strains of 1.1 and 1.0%, respectively. The COS and cohesive strength
of GZO are relatively similar to those reported in the literature for other polycrystalline
conducting films [15].

Summary

The material, opto-electrical properties, COS, the coating cohesive strength, as well
as the influence of mechanical strain on the electrical properties of nc GZO thin
films were investigated. The estimated average crystalline size of nc-GZO films was
approx. 8.7 nm, and the bandgap shifted from 3.73 eV (0.41 Pa) to 3.48 eV (0.86 Pa),
where the low resistivity (approx. 10-4 Ω cm) and the high electron density (>1020 cm-3) explain the dominating scattering process as the ionized impurity scattering. The
COS is similar for different GZO coatings and occurs for nominal strains approx. 1%.
The cohesive strength of coatings, which was evaluated from the initial part of the
crack density evolution, was found to be between 1.3 and 1.4 GPa, while the Young's
modulus was evaluated by nanoindentation.

Abbreviations

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

LR and SLM proposed the research work, and with APS coordinated the collaborations
and carried out the analysis and interpretation of the experimental results. VG and
LRP participated in sample processing, electromechanical experimental measurements,
and analysis and interpretation of the results. PA, AVK and YAD carried out electrical
measurements and SC performed the nanoindentation measurements. All authors read and
approved the final manuscript.

Acknowledgements

The authors acknowledge the receipt of funding from the Portuguese Foundation for
Science and Technology (FCT) Grant PTDC/CTM/69316/2006, INL project 156: SIMBIO, NANO/NMed-SD/0156/2007
and the CIENCIA 2007 programme.